Problem: Multiply the following complex numbers, marked as blue dots on the graph: $( e^{\pi i / 3}) \cdot (2 e^{2\pi i / 3})$ (Your current answer will be plotted in orange.)
Answer: Multiplying complex numbers in polar forms can be done by multiplying the lengths and adding the angles. The first number ( $ e^{\pi i / 3}$ ) has angle $\frac{1}{3}\pi$ and radius $1$ The second number ( $2 e^{2\pi i / 3}$ ) has angle $\frac{2}{3}\pi$ and radius $2$ The radius of the result will be $1 \cdot 2$ , which is $2$ The angle of the result is $\frac{1}{3}\pi + \frac{2}{3}\pi = \pi$ The radius of the result is $2$ and the angle of the result is $\pi$.